Factor completely. $4x^2+36xy+81y^2=$
$\begin{aligned} &\phantom{=}4 x ^2 + 36 x y + 81 y ^2 \\\\ &= ({2 x })^2 + 2({2 x })({9 y })+({9 y })^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({2 x })^2 + 2({2 x })({9 y })+({9 y })^2 \\\\ &=({2 x } + {9 y })^2 \end{aligned}$ In conclusion, $4 x ^2 + 36 x y + 81 y ^2=(2 x + 9 y )^2$ Remember that you can always check your factorization by expanding it.